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Econometrics 2015, 3(2), 317-338; doi:10.3390/econometrics3020317

The SAR Model for Very Large Datasets: A Reduced Rank Approach

National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, Australia
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Academic Editor: Giuseppe Arbia
Received: 12 January 2015 / Revised: 17 April 2015 / Accepted: 29 April 2015 / Published: 11 May 2015
(This article belongs to the Special Issue Spatial Econometrics)
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Abstract

The SAR model is widely used in spatial econometrics to model Gaussian processes on a discrete spatial lattice, but for large datasets, fitting it becomes computationally prohibitive, and hence, its usefulness can be limited. A computationally-efficient spatial model is the spatial random effects (SRE) model, and in this article, we calibrate it to the SAR model of interest using a generalisation of the Moran operator that allows for heteroskedasticity and an asymmetric SAR spatial dependence matrix. In general, spatial data have a measurement-error component, which we model, and we use restricted maximum likelihood to estimate the SRE model covariance parameters; its required computational time is only the order of the size of the dataset. Our implementation is demonstrated using mean usual weekly income data from the 2011 Australian Census. View Full-Text
Keywords: asymmetric spatial dependence matrix; Australian census; heteroskedasticity; Moran operator; spatial autoregressive model; spatial basis functions; spatial random effects model asymmetric spatial dependence matrix; Australian census; heteroskedasticity; Moran operator; spatial autoregressive model; spatial basis functions; spatial random effects model
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Burden, S.; Cressie, N.; Steel, D.G. The SAR Model for Very Large Datasets: A Reduced Rank Approach. Econometrics 2015, 3, 317-338.

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